Magnetic resonance (MR) imaging is a known technology that can produce images of the inside of an examination subject without radiation exposure. In a typical MR imaging procedure, the subject is positioned in a strong, static, homogeneous base magnetic field BO (having a field strength that is typically between about 0.5 Tesla and 3 Tesla) in an MR apparatus, so that the subject's nuclear spins become oriented along the base magnetic field.
Radio-frequency (RF) excitation pulses are directed into the examination subject to excite nuclear magnetic resonances, and subsequent relaxation of the excited nuclear magnetic resonances can generate RF signals. Rapidly switched magnetic gradient fields can be superimposed on the base magnetic field, in various orientations, to provide spatial coding of the RF signal data (also referred to as image data). The RF signal data can be detected during a ‘readout’ phase, and mathematically processed to reconstruct images of the examination subject. For example, the acquired RF signal data are typically digitized and stored as complex numerical values in a k-space matrix. An associated MR image can be reconstructed from the k-space matrix populated with such values using a multi-dimensional Fourier transformation.
FIG. 1 schematically shows the design of a magnetic resonance system 1 with certain components in accordance with embodiments of the present disclosure. The MR system 1 is configured, inter alia, to provide various magnetic fields tuned to one another as precisely as possible in terms of their temporal and spatial characteristics to facilitate examination of portions of a subject's body using magnetic resonance imaging techniques.
A strong magnet 5 (typically a cryomagnet) having a tunnel-shaped opening is provided in a radio-frequency (RF) shielded measurement chamber 3 to generate a static, strong base (or polarizing) magnetic field 7. The strength of the base magnetic field 7 is typically between 0.5 Tesla and 3 Tesla, although lower or higher field strengths can be provided in certain embodiments. A body or a body part to be examined (not shown) can be positioned within the substantially homogeneous region of the base magnetic field 7, e.g., provided on a patient bed 9.
Excitation of nuclear spins of certain atoms within the body can be provided via magnetic RF excitation pulses that are radiated using an RF antenna 13, such as a body coil. Other configurations of RF coils or antennas can also be provided in further embodiments, and such configurations may be adapted for particular portions of the subject anatomy to be imaged. The RF excitation pulses are generated by a pulse generation unit 15 that is controlled by a pulse sequence control unit 17. After an amplification by a radio-frequency amplifier 19, the RF pulses are relayed to the RF antenna 13. The exemplary RF system shown in FIG. 1 is a schematic illustration, and particular configurations of the various components may vary from that illustrated in exemplary embodiments of the disclosure. For example, the MR system 1 can include a plurality of pulse generation units 15, a plurality of RF amplifiers 19, and/or a plurality of RF antennas 13 that may have different configurations depending on the body parts being imaged.
The magnetic resonance system 1 further includes gradient coils 21 that can provide directionally and temporally varied magnetic gradient fields for selective excitation and spatial encoding of the RF signals that are emitted and/or received by the RF antenna(s) 13. The gradient coils 21 are typically oriented along the three primary axes (x- y- and z-directions), although other or additional orientations may be used in certain embodiments. Pulsed current supplied to the gradient coils 21 can be controlled by a gradient coil control unit 23 that, like the pulse generation unit 15, is connected with the pulse sequence control unit 27. By controlling the pulsed current supplied to the gradient coils 21, transient gradient magnetic fields in the x-, y-, and z-directions can be superimposed on the static base magnetic field BO. This makes it possible to set and vary, for example, the directions and magnitudes of a slice gradient magnetic field Gs, a phase encode gradient magnetic field Ge, and a read (frequency encode) gradient magnetic field Gr, which can be synchronized with emission and detection of RF pulses. Such interactions between RF pulses and transient magnetic fields can provide spatially selective excitation and spatial encoding of RF signals.
RF signals emitted by the excited nuclear spins can be detected by the RF antenna 13 and/or by local coils 25, amplified by associated radio-frequency preamplifiers 27, and processed further and digitized by an acquisition unit 29. In certain embodiments where a coil 13 (such as, for example, a body coil) can be operated both in transmission mode and in acquisition mode (e.g, it can be used to both emit RF excitation pulses and receive RF signals emitted by nuclear spins), the correct relaying of RF energy is regulated by an upstream transmission-reception diplexer 39.
An image processing unit 31 can generate one or more images based on the RF signals that represent image data. Such images can be presented to a user via an operator console 33 and/or be stored in a memory unit 35. A processor arrangement 37 can be provided in communication with the memory unit 35, and configured to execute computer-executable instructions stored in the memory unit 35 to control various individual system components. For example, the processor arrangement 37 can be configured by programmed instructions to control components such as, e.g., the gradient coil control unit 23, the pulse generation unit 15, and/or the pulse sequence control unit 27 to generate particular sequences of RF pulses and magnetic field variations, process and/or manipulate image data, etc., according to exemplary embodiments of the disclosure described herein.
Magnetic resonance imaging is a versatile modality which allows not only qualitative organ or tissue anatomical evaluation but also quantitative assessment of tissue characteristics. For example, diffusion MRI, which includes diffusion-weighted imaging (DWI) and diffusion tensor imaging (DTI), is a quantitative imaging technique that can provide certain quantitative information on specific features of imaged tissues.
Diffusion MRI is generally based on the Brownian motion of water molecules. It can provide certain contrasts and characterizations among tissues at a cellular level in vivo and non-invasively. Because the diffusion rate of water molecules in different tissues correlates with their physiological state, and may be altered in diseased tissues, DWI has a very important role in clinical applications. For example, an early and widely-used application of DWI is to diagnose acute ischemic stroke in the brain.
In diffusion-weighted (DW) images, the intensity of each pixel reflects an estimate of the water diffusion rate at that pixel, and also the tissue structure in which the water molecules diffuse. This pixel intensity is attenuated according to the diffusion weighting (b-value) and direction of the diffusion gradients. The DW image intensity can be described by the Intra Voxel Incoherent Motion (IVIM) model, where both the pure molecular-based diffusion process and the perfusion-based diffusion process related with the incoherent microcirculation contribute to the signal attenuation, where this signal attenuation has been observed to exhibit an approximately exponential decay. The IVIM model is described, e.g., in LeBihan D, Breton E, Lallemand D, Aubin M L, Vignaud J, Laval-Jeantet M., “Separation of diffusion and perfusion in intravoxel incoherent motion MR imaging,” Radiology 1988; 168:497-505.
In practice, if two or more DW images with different b-values are acquired, a so-called apparent diffusion coefficient (ADC) map can be calculated as a single “effective” coefficient to simplify the characterization of different mechanisms in the diffusion process. The ADC corresponds to the exponential coefficient in the signal model describing signal loss with increasing b value. Unlike individual DW images, the ADC map is insensitive to the influence of T1 and T2/T2* effects and provides voxel-by-voxel ADC values as a property of the tissue; thus the ADC is regarded as a quantitative measure of the diffusion behavior in tissue. Further, ADC maps can be averaged from three orthogonal orientations to yield an overall ADCtrace map, which further removes diffusion orientation dependence.
The signal-to-noise ratio (SNR) tends to be relatively low in DW images as compared to other image contrasts, in large part because of T2/T2* effects and the diffusion weighting. This low SNR poses a challenge for ADC quantification, as the SNR of high b-value DW images may be close to or below the noise floor. In practice, high b-values often have to be used, and low SNR cannot be avoided. In addition, some organs such as the liver typically have a lower SNR in high b-value DW images than other anatomic regions. The noise in the high b-value images, if not accounted for, can lead to significant errors in the resultant ADC map.
Several factors can affect the SNR during acquisition of MR image data, many of which can be controlled or selected by an operator. These factors include image resolution (e.g., slice thickness, size of the image matrix, and field of view), scan parameters (such as TR, TE, and flip angle), magnetic field strength, and coil selection/geometry.
For example, it is generally observed that the SNR in MR imaging will increase with decreasing resolution of the image data. Larger SNR values can lead to more accurate calculation of ADC values and other quantitative MR imaging parameters. However, the decreased image resolution is generally undesirable. For example, decreased image resolution (which corresponds to larger pixels or voxels) may fail to sufficiently distinguish tissue features and variations in the imaged region. Further, because parameters such as the ADC typically are dependent in part on tissue type, low-resolution/high-SNR image data can fail to properly measure localized values of such parameters, e.g., averaging different values of the ADC from different tissues present in a single pixel/voxel. This undesirable spatial averaging can inhibit or prevent obtaining of an accurate ADC map having sufficient spatial resolution. Thus, there is an inherent trade-off between decreasing the spatial resolution of the DW image data to increase the SNR, and decreasing the localization and accurate spatial variations of the parameters to be determined (such as the ADC), thereby resulting in less-accurate parameter maps.
Similarly, other quantitative techniques in MRI are also influenced by the noise effects. Such quantitative property maps include, but are not limited to, calculated T2, R2, T2* or R2* maps using spin echo (SE), turbo/fast spin echo (TSE/FSE) or gradient echo (GRE) MRI, respectively, calculated T1 maps using SE, TSE/FSE or Turbo FLASH MRI, and calculated proton density fat fraction (PDFF) and proton density water fraction (PDWF) maps using GRE MRI. Although the present disclosure primarily focuses on calculations and results relating to ADC measurement and values, the same approach and methods can be used for other quantitative MRI procedures such as those mentioned above.
Background Theory
To provide a more complete basis for understanding the inventive systems and methods described herein, an overview of the basic equations of the signal model for calculating ADC values using quantitative MRI will now be summarized. First, for the MR image data acquisitions used to calculate an ADC map, all imaging parameters except the b-values, e.g. TR and TE, are kept essentially constant so that common factors such as T1 and T2/T2* effects can be ignored in the signal model. For the n acquisitions with varying b-values, the general equations of the acquired MR signal are given byS1=S0e−b1·ADC . . . ,Sn=S0e−bn·ADC  [1]where S0 represents a voxel intensity without diffusion weighting, e.g., with b=0. The set of equalities in Equation [1] has two unknown variables, S0 and ADC, and these values can be determined using at least two DW MR image acquisitions obtained with different b-values.
Various techniques for fitting MR diffusion data to obtain an ADC map have been described in the literature and used in practice. The most widely accepted method is the log-linear (LL) fitting method. By taking the log of both sides of Eq. [1], and defining yi asyi=log(Si),  [2]
Eq. [1] can be written in the formy1=log(S0)−ADC·b1 . . .yn=log(S0)−ADC·bn  [3]If we further define:xi=bi,  [4]
                                          y            _                    =                                                    ∑                                  i                  =                  1                                n                            ⁢                              y                i                                      n                          ,                            [        5        ]            and
                                          x            _                    =                                                    ∑                                  i                  =                  1                                n                            ⁢                              x                i                                      n                          ,                            [        6        ]            then the ADC can be calculated as
                    ADC        =                                                            n                ⁢                                  x                  _                                ⁢                                  y                  _                                            -                                                ∑                                      i                    =                    1                                    n                                ⁢                                                      x                    i                                    ⁢                                      y                    i                                                                                                                        ∑                                      i                    =                    1                                    n                                ⁢                                  x                  i                  2                                            -                              n                ⁢                                                      x                    _                                    2                                                              .                                    [        7        ]            
Another common approach for solving for the unknown variables in non-linear equations is the least-squares (LS) non-linear fitting method. The least-squares non-linear fitting method can be summarized as a solution that minimizes the sum of the squares of the errors (E) for the fitted data points. For example, the LS method can be used to determine the two unknown variables in Equation [1], S0 and ADC, by minimizing E, where E is defined as
                              E          =                                    ∑                              i                =                1                            n                        ⁢                                                                                                S                    i                                    -                                      F                    i                                                                              2                                      ,                            [        8        ]            and where Fi is defined asFi=m0(bi),  [9]withm0(bi)=S0e−bi·ADC.  [10]
With sets of diffusion image data obtained using at least two different b-values, there are various least squares non-linear techniques known in the art (and in the general field of nonlinear mathematics) that can be used to determine values of S0 and ADC that minimize E in Equation [8]. For example, the Levenberg-Marquardt algorithm, also known as the damped least-squares method, can be used. Other conventional least-squares solution techniques may also be used to solve Equation [8].
Signal intensities in an MR image are often corrupted by noise. In MRI image data, which is naturally complex data, the noise distribution has generally been observed to be well-represented by a symmetrical Gaussian or normal distribution. However, in DWI procedures, only the magnitude of the signal data is typically used in ADC calculations, e.g., the Si values represent only the magnitude without the phase. This conversion from complex data to magnitude values causes the noise distribution for the magnitude data to be changed to an asymmetric Rician distribution, or more generally, non-central chi-squared distribution for multi-channel coils. As a result, signal intensities at low SNR can exhibit a systematic bias related to the noise, the magnitude of which appears as a value (mbias) that is higher than the noise-free true value of the magnitude (m0). If this effect is not properly accounted for, the fitted estimates of the ADC will tend to be biased when the SNR of the obtained image data is low.
U.S. Patent Publication No. 2016/0084929 of Dale et al. describes a technique to correct such noise effects for signal magnitude data that includes three different noise-biased data models (mMP, mMD and mEX) and two different approaches for processing the noise-biased data (referred to therein as the Forward Approach and the Backward Approach). In the present disclosure, mMP and the Backward Approach are used, in addition to the log-linear and least-squares fitting techniques described herein above, to further illustrate examples of the methods described herein.
In practice, multiple DW image datasets corresponding to a high b-value can be obtained and averaged. Such averaging can increase the effective SNR (e.g., by averaging out some of the noise effects) such that the averaged high b-value DW image data can have sufficient SNR to perform fitting methods such as LL and LS more accurately. However, this averaging approach suffers from a bias in the resultant ADC value, because the source data of the high b-value DW images are contaminated by noise having a non-zero expectation value. Thus, the averaged images (typically averaged using the magnitude images of all the repetitions obtained for a particular b-value) still exhibit systematic errors in the image intensity.
Accordingly, it would be desirable to have a method for improved quantitative MRI in which the effects of inherent signal noise on measured parameters for a particular fitting scheme can be better predicted. Such information can be used, e.g., to facilitate acquisition of improved parameter maps by selection of optimal imaging parameters and/or to generate improved parameter maps directly by applying such predicted noise effects to the fitted/calculated parameter values.